The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the arrow of time without a Past Hypothesis, i.e. the assumption of a special initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We (...) then propose a definition of a Boltzmann entropy for a classical N-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational. (shrink)

The paper provides a critical discussion of the Super-Humean view of spacetime and the “minimalist ontology” in terms of Leibnizian relations and primitive matter points, recently developed by Esfeld et al. It investigates, in particular, the empirical adequacy of the proposed metaphysics, arguing that Super-Humeanism cannot provide a plausible account of space and time without committing to bona fide geometric structure in the fundamental relations. Against this backdrop, I propose a moderate version of Super-Humeanism and discuss its possible application to (...) Euclidean space and General Relativity. (shrink)

I present an argument for the view that laws ground their instances. I then outline two important consequences that follow if we accept the conclusion of this argument. First, the claim that laws ground their instances threatens to undermine a prominent recent attempt to make sense of the explanatory power of Humean laws by distinguishing between metaphysical and scientific explanation. And second, the claim that laws ground their instances gives rise to a novel argument against the view that grounding relations (...) are metaphysically necessary. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...) of probability in explanation and laws. This is the 'paradox of deterministic probabilities'. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics. (shrink)

Tim Maudlin has influentially argued that Humeanism about laws of nature stands in conflict with quantum mechanics. Specifically Humeanism implies the principle Separability: the complete physical state of a world is determined by the intrinsic physical state of each space-time point. Maudlin argues Separability is violated by the entangled states posited by QM. We argue that Maudlin only establishes that a stronger principle, which we call Strong Separability, is in tension with QM. Separability is not in tension with QM. Moreover, (...) while the Humean requires Separability to capture the core tenets of her view, there's no Humean-specific motivation for accepting Strong Separability. We go on to give a Humean account of entangled states which satisfies Separability. The core idea is that certain quantum states depend upon the Humean mosaic in much the same way as the laws do. In fact, we offer a variant of the Best System account on which the systemization procedure that generates the laws also serves to ground these states. We show how this account works by applying it to the example of Bohmian Mechanics. The 3N-dimensional configuration space, the world particle in it and the wave function on it are part of the best system of the Humean mosaic, which consists of N particles moving in 3-dimensional space. We argue that this account is superior to the Humean account of Bohmian Mechanics defended by Loewer and Albert, which takes the 3N-dimensional space, and its inhabitants, as fundamental. (shrink)

David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world (...) supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws. (shrink)

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the (...) law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)

It has often been argued that Humean accounts of natural law cannot account for the role played by laws in scientific explanations. Loewer (Philosophical Studies 2012) has offered a new reply to this argument on behalf of Humean accounts—a reply that distinguishes between grounding (which Loewer portrays as underwriting a kind of metaphysical explanation) and scientific explanation. I will argue that Loewer’s reply fails because it cannot accommodate the relation between metaphysical and scientific explanation. This relation also resolves a puzzle (...) about scientific explanation that Hempel and Oppenheim (Philosophy of Science 15:135–75, 1948) encountered. (shrink)

Among the most important questions in the metaphysics of science are "What are the natures of fundamental laws and chances?" and "What grounds the direction of time?" My aim in this paper is to examine some connections between these questions, discuss two approaches to answering them and argue in favor of one. Along the way I will raise and comment on a number of issues concerning the relationship between physics and metaphysics and consequences for the subject matter and methodology of (...) metaphysics. (shrink)

In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating roller-coaster ride through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.

I want to defend a Combinatorialtheory of possibility. Such a view traces the very idea of possibility to the idea of the combinations – all the combinations which respect a certain simple form – of given, actual, elements. Combination is to be understood widely enough to cover the notions of expansion and contraction. The combinatorial idea is not new, of course. Wittgenstein gave a classical exposition of it in the Tractatus. Perhaps its charter is 3.4: ‘A proposition determines a place (...) in logical space. The existence of this logical place is guaranteed by the mere existence of the constituents’. There is a small additional combinatorial literature. I myself was converted to a combinatorial view by Brian Skyrms’ brief but fascinating article ‘Tractarian Nominalism.’. (shrink)

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, (...) of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the ...

This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and (...) sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text. (shrink)

In this sequence of philosophical essays about natural science, the author argues that fundamental explanatory laws, the deepest and most admired successes of modern physics, do not in fact describe regularities that exist in nature. Cartwright draws from many real-life examples to propound a novel distinction: that theoretical entities, and the complex and localized laws that describe them, can be interpreted realistically, but the simple unifying laws of basic theory cannot.

Suppose that God or a demon informs you of the following future fact: despite recent cosmological evidence, the universe is indeed closed and it will have a ‘final’ instant of time; moreover, at that final moment, all 49 of the world’s Imperial Faberge eggs will be in your bedroom bureau’s sock drawer. You’re absolutely certain that this information is true. All of your other dealings with supernatural powers have demonstrated that they are a trustworthy lot.

Perhaps the most significant contemporary theory of lawhood is the Best System (/MRL) view on which laws are true generalizations that best systematize knowledge. Our question in this paper will be how best to formulate a theory of this kind. We’ll argue that an acceptable MRL should (i) avoid inter-system comparisons of simplicity, strength, and balance, (ii) make lawhood epistemically accessible, and (iii) allow for laws in the special sciences. Attention to these problems will bring into focus a useful menu (...) of novel MRL theories, some of which solve problems the original MRL theory could not. Hence we conceive of the paper as moving toward a better Best System theory of laws. (shrink)

John Carroll undertakes a careful philosophical examination of laws of nature, causation, and other related topics. He argues that laws of nature are not susceptible to the sort of philosophical treatment preferred by empiricists. Indeed he shows that emperically pure matters of fact need not even determine what the laws are. Similar, even stronger, conclusions are drawn about causation. Replacing the traditional view of laws and causation requiring some kind of foundational legitimacy, the author argues that these phenomena are inextricably (...) intertwined with everything else. This distinctively clear and detailed discussion of what it is to be a law will be valuable to a broad swathe of philosophers in metaphysics, the philosophy of mind, and the philosophy of science. (shrink)

The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. The Leibnizian biconditionals relate possibility and necessity to possible world and true in.

A version of relationism that takes spatiotemporal structures—spatial geometry and a standard of inertia—to supervene on the history of relations between bodies is described and defended. The account is used to explain how the relationist should construe models of Newtonian mechanics in which absolute acceleration manifestly does not supervene on the relations; Ptolemaic and Copernican models for example. The account introduces a new way in which a Lewis-style ‘best system’ might capture regularities in a broadly Humean world; a defence is (...) given against a charge of indeterminism that applies to any such approach to laws. (shrink)

What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to it.

It is a traditional empiricist doctrine that natural laws are universal truths. In order to overcome the obvious difficulties with this equation most empiricists qualify it by proposing to equate laws with universal truths that play a certain role, or have a certain function, within the larger scientific enterprise. This view is examined in detail and rejected; it fails to account for a variety of features that laws are acknowledged to have. An alternative view is advanced in which laws are (...) expressed by singular statements of fact describing the relationship between universal properties and magnitudes. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

Non-Humean accounts of lawhood are said to founder on the Inference Problem, which is the problem of saying how laws that go beyond the regularities can entail the regularities. I argue that the Inference Problem has a simple solution – the Axiomatic Solution – on which the non-Humean only needs to outfit her laws with a law-to-regularity axiom. There is a remaining Epistemic Bulge, as to why one should believe that the posit-so-axiomatized is to be found in nature, but the (...) non-Humean can flatten the bulge. Lawhood serves as a case study of how fundamental posits can do their business. (shrink)

This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...) decision. Throughout, Lewis analyzes global features of the world in such a way as to show that they might turn out to supervene on the spatiotemporal arrangement of local qualities. (shrink)

Here the philosopher and physicist David Z Albert argues, among other things, that the difference between past and future can be understood as a mechanical phenomenon of nature and that quantum mechanics makes it impossible to present the entirety of what can be said about the world as a narrative of “befores” and “afters.”.

Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

John Foster presents a clear and powerful discussion of a range of topics relating to our understanding of the universe: induction, laws of nature, and the existence of God. He begins by developing a solution to the problem of induction - a solution whose key idea is that the regularities in the workings of nature that have held in our experience hitherto are to be explained by appeal to the controlling influence of laws, as forms of natural necessity. His second (...) line of argument focuses on the issue of what we should take such necessitational laws to be, and whether we can even make sense of them at all. Having considered and rejected various alternatives, Foster puts forward his own proposal: the obtaining of a law consists in the causal imposing of a regularity on the universe as a regularity. With this causal account of laws in place, he is now equipped to offer an argument for theism. His claim is that natural regularities call for explanation, and that, whatever explanatory role we may initially assign to laws, the only plausible ultimate explanation is in terms of the agency of God. Finally, he argues that, once we accept the existence of God, we need to think of him as creating the universe by a method which imposes regularities on it in the relevant law-yielding way. In this new perspective, the original nomological-explanatory solution to the problem of induction becomes a theological-explanatory solution. The Divine Lawmaker is bold and original in its approach, and rich in argument. The issues on which it focuses are among the most important in the whole epistemological and metaphysical spectrum. (shrink)

This book provides an account of the nature of time, especially time's arrow and the role of entropy, at a semi-popular level. Special attention is given to statistical mechanics, the past hypothesis, and possible cosmological explanations thereof.

In recent literature, it has become clear that quantum physics does not refute Humeanism: Lewis’s thesis of Humean supervenience can be literally true even in the light of quantum entanglement. This point has so far been made with respect to Bohm’s quantum theory. Against this background, this paper seeks to achieve the following four results: to generalize the option of quantum Humeanism from Bohmian mechanics to primitive ontology theories in general; to show that this option applies also to classical mechanics; (...) to establish that it requires a commitment to matter as primitive stuff, but no commitment to natural properties ; to point out that by removing the commitment to properties, the stock metaphysical objections against Humeanism from quidditism and humility no longer apply. In that way, quantum physics strengthens Humeanism instead of refuting it. (shrink)

One reason to posit governing laws is to explain the uniformity of nature. Explanatory power can be purchased by accepting new primitives, and scientists invoke laws in their explanations without providing any supporting metaphysics. For these reasons, one might suspect that we can treat laws as wholly unanalyzable primitives. (John Carroll’s *Laws of Nature* (1994) and Tim Maudlin’s *The Metaphysics Within Physics* (2007) offer recent defenses of primitivism about laws.) Whatever defects primitive laws might have, explanatory weakness should not be (...) one of them. However, in this essay I’ll argue that wholly primitive laws cannot explain the uniformity of nature. The basic argument is based on the following idea: though a primitive law that P makes P likely, the primitive status of the law provides no reason to think that P must describe (or otherwise give rise to) a natural regularity. After identifying the problem for primitive laws, I consider an extension of the objection to all theories of governing laws and suggest that it may be avoided by a version of the Dretske/Tooley/Armstrong theory according to which laws are relations between universals. (shrink)